Bayesian optimization of atomic structure for collisional calculations

Accurate computation of collisional rates requires a precise description of the ionic targets involved. However, obtaining an adequate atomic structure often entails significant computational effort. The optimization of target wavefunctions typically relies on configuration interaction (CI) expansions, where additional configurations are included to improve accuracy. The radial orbitals are generated using model potentials that depend on adjustable scaling parameters, whose variation can produce erratic behavior in the results. Consequently, the lack of a systematic procedure for parameter tuning remains a major limitation.

In this work, we implement a Bayesian optimization approach based on Gaussian processes (GPs) to refine the atomic structure of ions. This machine learning technique efficiently minimizes scalar-valued error functions and provides a data-driven framework for systematic optimization. The methodology can be extended from scalar-valued to multi-objective (vector-valued) optimization to simultaneously improve several atomic properties such as energies and oscillator strengths. The scaling parameters of the model potentials are treated as variables within the Bayesian framework, allowing automatic exploration of the parameter space.

The atomic structures of Be and Mg are calculated using the AUTOSTRUCTURE code [1]. The resulting energies and oscillator strengths of the lowest-lying terms show agreement with experimental values within 1% and 10%, respectively, demonstrating the efficiency of the proposed method. The optimized atomic structures obtained are tested by comparing our electron impact excitation results with benchmark results [1, 2, 3]. This approach was proven to provide a robust and general tool for optimizing atomic structure calculations in collisional studies.

References:
[1] Badnell N R 2011 Comput. Phys. Commun. 7 1528
[1] Zatsarinny O et al. 2016 J. Phys. B 49 235701
[2] Ballance C P et al. 2003 Phys. Rev. A 68 062705
[3] Barklem, P. S., Osorio, Y., Fursa, D. V., et al. 2017, A&A, 606, A11